Problem: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-x-2y &= 1 \\ 7x+9y &= 3\end{align*}$
Explanation: Begin by moving the $x$ -term in the second equation to the right side of the equation. $9y = -7x+3$ Divide both sides by $9$ to isolate $y$ $y = {-\dfrac{7}{9}x + \dfrac{1}{3}}$ Substitute this expression for $y$ in the first equation. $-x-2({-\dfrac{7}{9}x + \dfrac{1}{3}}) = 1$ $-x + \dfrac{14}{9}x - \dfrac{2}{3} = 1$ Simplify by combining terms, then solve for $x$ $\dfrac{5}{9}x - \dfrac{2}{3} = 1$ $\dfrac{5}{9}x = \dfrac{5}{3}$ $x = 3$ Substitute $3$ for $x$ back into the top equation. $- 3-2y = 1$ $-3-2y = 1$ $-2y = 4$ $y = -2$ The solution is $\enspace x = 3, \enspace y = -2$.